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Simplifying 4a2 + 12a + 9 = 144 Reorder the terms: 9 + 12a + 4a2 = 144 Solving 9 + 12a + 4a2 = 144 Solving for variable 'a'. Reorder the terms: 9 + -144 + 12a + 4a2 = 144 + -144 Combine like terms: 9 + -144 = -135 -135 + 12a + 4a2 = 144 + -144 Combine like terms: 144 + -144 = 0 -135 + 12a + 4a2 = 0 Factor a trinomial. (-15 + -2a)(9 + -2a) = 0Subproblem 1
Set the factor '(-15 + -2a)' equal to zero and attempt to solve: Simplifying -15 + -2a = 0 Solving -15 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2a = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2a = 0 + 15 -2a = 0 + 15 Combine like terms: 0 + 15 = 15 -2a = 15 Divide each side by '-2'. a = -7.5 Simplifying a = -7.5Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve: Simplifying 9 + -2a = 0 Solving 9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a = 0 + -9 -2a = 0 + -9 Combine like terms: 0 + -9 = -9 -2a = -9 Divide each side by '-2'. a = 4.5 Simplifying a = 4.5Solution
a = {-7.5, 4.5}
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